Problem: Simplify the following expression: $\dfrac{121p^4}{33p}$ You can assume $p \neq 0$.
$ \dfrac{121p^4}{33p} = \dfrac{121}{33} \cdot \dfrac{p^4}{p} $ To simplify $\frac{121}{33}$ , find the greatest common factor (GCD) of $121$ and $33$ $121 = 11 \cdot 11$ $33 = 3 \cdot 11$ $ \mbox{GCD}(121, 33) = 11 $ $ \dfrac{121}{33} \cdot \dfrac{p^4}{p} = \dfrac{11 \cdot 11}{11 \cdot 3} \cdot \dfrac{p^4}{p} $ $\phantom{ \dfrac{121}{33} \cdot \dfrac{4}{1}} = \dfrac{11}{3} \cdot \dfrac{p^4}{p} $ $ \dfrac{p^4}{p} = \dfrac{p \cdot p \cdot p \cdot p}{p} = p^3 $ $ \dfrac{11}{3} \cdot p^3 = \dfrac{11p^3}{3} $